I think people are afraid that someone not 100% in charge of his healthy reasoning faculties will respond the wrong way in a social situation. Like, stabbing you thirteen times in the chest for being a Spawn of Satan, if you happen to ask them what time the #33 bus shows up.
(Geez, just because you say have schizophrenia, they call you a "psycho"!--Totally different thing!)
Even the old ladies on the street, who scream obscenities at strangers or at no one in particular, are socially avoided because of our basic "stigma"--Yes, not all mentally ill people are homeless, but OTOH...

Perhaps it dates back to that Alice sentiment about "not wanting to go among mad people".

I believe the first issue starts with the fact that everyone, both non-mentally ill and mentally ill, separate being mentally ill off as a "type" to begin with. Looking at it through black and white lenses, is the first step to the subconscious separation between people. No one's brain chemicals are 100% perfect; so we're all just a little bit mentally ill.

Secondly, as someone who has been diagnosed with Manic Depression, and several others, since I was an adolescent teen, I can say it never gets easy. There are periods that are okay and periods that really really aren't okay. There are plenty of people out there that are willing to understand, and even more out there that won't. Out of the people that won't understand, or atleast try, there's people who're simply biased and then there's people that have had some bad encounters with mentally ill people and become set in their opinion for the rest of them.

Though the biases against mentally ill people aren't helped by the fact that there ARE some that use it as an excuse to not even try to act civilized, and some that use it as a tasteless cry for attention.

Its really hard to understand mental illness for a lot of people, including myself. Trying to put myself in a someone else's shoes, I find myself staring at the ways out I would take. Back in High School, for a while I was extremely depressed, but I re-evaluated my life and stepped forward. That is most people's experience with the symptoms of these disorders, especially depression. They feel down for a little while but they get past it, and because of that, it is difficult to empathize with those who cannot get out of it because of a chemical imbalance. That leads you to feel as if they are doing something wrong or choosing to not take that step forward, whether or not that is true. You need to understand that these people are usually not acting this way due to any ill will, but because they cannot fathom an existence in which these disorders exist inside them.

You also have to realize that, regardless of disorders, it can be really difficult to be around people with mental disorders. It can be extremely exhausting, physically and emotionally and I don't think you can blame them for distancing themselves when so many interactions turn into something negative. People don't like being around someone who can ruin a day on a whim, regardless of illness. While in a perfect world, they would be there for you (and in my experience, they are usually trying their best even if you don't see it), you also need to realize that no one can take these steps forward to bettering yourself but you. Whether that means learning how to control yourself, speaking to a professional or starting medication, it is on you.

Plus, even mentally ill people can find themselves judging or frustrated with other mentally ill people. It's not something only subject to people who don't understand. Sundin13 is 100% right in saying that getting better is on you. It's your brain. Your actions. Your choices. There is no fairy godmother to wave a sparkly stick around and magically make everything all better.